A general approach to the description of effective states of heavy atoms in molecules and solids in terms of fractional-occupancy relativistic configurations in the frames of the new Atoms-in-Compounds (AiC) concept is discussed. This approach is based on the analysis of molecular one-electron density matrices in the vicinity of heavy nuclei and the
simulation of the basic features of these entities in free or constrained heavy atom calculations. The resulting configurations are related to some measurable (spectral) properties of the compounds. A series of applications to simple compounds of early transuranium elements and superheavy elements 112-114 is presented. The results are
compared to those obtained by the projection technique.